Answer :
To find the next two terms in the sequence [tex]\(5, 25, 125, 625, \ldots\)[/tex], let's first observe the pattern.
1. Identify the Pattern: Look at the numbers. Each number seems to be multiplied by the same value to get the next number:
- [tex]\(5 \times 5 = 25\)[/tex]
- [tex]\(25 \times 5 = 125\)[/tex]
- [tex]\(125 \times 5 = 625\)[/tex]
This pattern indicates a common ratio, meaning this is a geometric sequence with a common ratio of 5.
2. Calculate the Next Terms:
- To find the term after 625, multiply 625 by the common ratio:
[tex]\[
625 \times 5 = 3125
\][/tex]
- Now, to find the term after 3125, multiply 3125 by the common ratio:
[tex]\[
3125 \times 5 = 15625
\][/tex]
3. Conclusion: So, the next two terms in the sequence are 3125 and 15625. Therefore, the complete sequence with these next terms is [tex]\(5, 25, 125, 625, 3125, 15625\)[/tex].
Based on the options given:
- 3125 and 15625 match with one of the listed answer choices.
So, the answer is:
3125, 15625
1. Identify the Pattern: Look at the numbers. Each number seems to be multiplied by the same value to get the next number:
- [tex]\(5 \times 5 = 25\)[/tex]
- [tex]\(25 \times 5 = 125\)[/tex]
- [tex]\(125 \times 5 = 625\)[/tex]
This pattern indicates a common ratio, meaning this is a geometric sequence with a common ratio of 5.
2. Calculate the Next Terms:
- To find the term after 625, multiply 625 by the common ratio:
[tex]\[
625 \times 5 = 3125
\][/tex]
- Now, to find the term after 3125, multiply 3125 by the common ratio:
[tex]\[
3125 \times 5 = 15625
\][/tex]
3. Conclusion: So, the next two terms in the sequence are 3125 and 15625. Therefore, the complete sequence with these next terms is [tex]\(5, 25, 125, 625, 3125, 15625\)[/tex].
Based on the options given:
- 3125 and 15625 match with one of the listed answer choices.
So, the answer is:
3125, 15625
